Halliday, Resnick & Walker — Rotation: Problem Problem_68

Two uniform solid spheres have the same mass of \(1.65\text{ kg}\), but one has a radius of \(0.226\text{ m}\) and the other has a radius of \(0.854\text{ m}\). Each can rotate about an axis through its center. (a) What is the magnitude \(\tau\) of the torque required to bring the smaller sphere from rest to an angular speed of \(317\text{ rad/s}\) in \(15.5\text{ s}\)? (b) What is the magnitude \(F\) of the force that must be applied tangentially at the sphere’s equator to give that torque? What are the corresponding values of (c) \(\tau\) and (d) \(F\) for the larger sphere?